Method of determining position of openings adapted to receive fret saw blade of numerically controlled fret saw machines

Abstract

In a machine for cutting grooves of a given pattern through a blank with a fret saw blade, openings for receiving the fret saw blade at the cutting starting points of the grooves are determined such that the center of each opening is positioned at a point spaced from a cutting start point by a distance equal to one half of the width of the fret saw blade in a direction opposite to the direction of cutting the groove.

What is claimed is: 
     
       1. In a numerically controlled fret saw machine comprising: blank drive means for clamping a flat plate shaped blank to move the same to any position on a X-Y plane of rectangular coordinates;   fret saw blade rotation means for controlling rotation of said fret saw blade such that a tip of said blade is normally oriented in directions of grooves cut through said blank by said fret saw blade;   a tool disposed on said X-Y plane with a predetermined spacing between the tool and the fret saw blade for forming openings through said blank;   drive means for driving said tool; and   a digital control device for controlling the direction of movements of said blank in X and Y axes directions of rectangular coordinates and for controlling rotation of said fret saw blade, thereby forming with said tool openings adapted to receive said fret saw blade at points respectively corresponding to cutting start points of said grooves,   a method of determining a position of each opening comprising the steps of:   producing a movement instruction data regarding a cutting start point and a cutting end point of a portion of a groove to be cut, said points defining a path A→B;   determining a point P having coordinates (XP·YP) and representing a center of said opening for receiving said fret saw blade, said point P being located on a straight line passing through a point A having coordinates (XA·YA) and a point B having coordinates (XB·YB) and said point P being spaced from said point A by one half of the width SW of said fret saw blade in a direction opposite to the direction of cutting of the groove starting from said point A when said section is straight, whereas when said section is a circular arc, said point P is selected to be a line which is tangent to said ciruclar arc at said point A and spaced from said point A by one half of the width SW of said fret saw blade.   
     
     
       2. The method according to claim 1 wherein the coordinates of said points P are determined by the steps of: I. calculating orientation angle θ of said fret saw blade at time of starting cutting from said point A in accordance with a cutting instruction data regarding a path of from said point A to said point B and temporarily storing said orientation angle and   II. calculating the coordinates (XP·YP) of said point P by using said orientation angle θ according to the following equations:   (A) where said path A→B is a straight line and where |XBUF|=|YBUF|,   XP=XA+(SX)·SW/2·cos θ       YP=YA+(SY)·SW/2·sin θ       whereas when |XBUF|<|YBUF|   XP=XA+(SX)·SW/2·sin θ       YP=YA+(SY)·SW/2·cos θ       (B) where said path A→B i s a circular arc and where |XBUF|≧|YBUF|   XP=XA+(SX)·SW/2·sin θ       YP=YA+(SY)·SW/2·cos θ       whereas when |XBUF<|YBUF|   XP=XA+(SX)·SW/2·cos θ       YP=YA+(SY)·SW/2·sin θ       wherein 0≦θ≦π/4 and XBUF and YBUF represent increments between point A(XA·YA) and point B(XB·YB) and expressed by equations XBUF=XB-XA and YBUF=YB-YA in the case of A, whereas in the case of B expressed by XBUF=i and YBUF=J where i and J represent coordinates of said point A from the center of said circular arc, and wherein (SX) and (SY) represent signs of X and Y components of a vector extending in a direction opposite to the orientation of said fret saw blade at said cutting starting point A and when said vector is in a first quadrant, expressed by     (SX)=+1, (SY)=+1     in a second quadrant, expressed by     (SX)=-1, (SY)=+1     in a third quadrant, expressed by     (SX)=-1, (SY)=-1 and     in a fourth quadrant expressed by     (SX)=+1, (SY)=-1.       
     
     
       3. The method according to claim 1 wherein when said path A→B is a straight line and cutting amounts of shifts XL' and YL' are calculated according to the following equations by using ##EQU10## when a movement instruction from said point A to said point B is given by an output format of G1 XL·YL (where XL and YL represent increments). 
     
     
       4. The method according to claim 1 wherein when said path A→B is a circular arc, the position of said opening is determined by the steps of: giving a movement information of from point A to point B as an output format   G2 XL·YL·i·J or       G3 XL·YL·i·J     determining a quadrant in which said point A resides according to written values of i and J,     judging whether said path A→B is clockwise (G2) or counterclockwise (G3) in accordance with given circular are cutting instruction codes (G2 and G3),   calculating a pair of values (SX) and (SY) determined by combining aforementioned formats,   calculating amounts of shifts according to the following equations by using values of i, J, (SX) and (SY) and tooth width SW ##EQU11## calculating   XP=XA+XL'       YP=YA+YL'     by using the values of XL' and YL' thus calculated.     
     
     
       5. The method according to claim 1 wherein when said path A→B is a straight line, the position of said opening is determined by the steps of: (1) determining coordinate values (XA1·YA1) and (XA2·YA2) of cross-points A1 and A2 between a straight line passing through said points A and B and a circle about said point A and having a radius of 1/2SW;   (2) judging YA1-YA2=0 regarding one coordinate axis, for example, axis Y;   (3) then, if YA1-YA2≠0 calculate the followings:   d=YB-YA       d1=YA-YA1       d2=YA-YA2;       (4) selecting one of d1 and d2 which has the same sign as d;   (5) setting   XP=XA1, YP=YA1        if the result of step (4) is d1, whereas setting   XP=XA2, YP=YA2        if the result is d2;   (6) determining   d=XB-XA       d1=XA-XA1       d2=XA-XA2        if at step 2 YA1-YA2=0; and   (7) then returning to step (4).   
     
     
       6. The method according to claim 1 wherein when the path A→B is a circular arc, the position of said opening is determined by the steps of: (1) determining the coordinate values (XA1·YA1) and (XA2·YA2) of cross-points A1 and A2 between a tangent line to a circle C1 including an arc AB and passing through point A and a circle C2 about point A and having a radius 1/2SW;   (2) determining coordinate values (XA3·YA3) and (XA4·YA4) of cross-points between said circules C1 and C2;   (3) determining number of pulses pA·B necessary to rotate said fret saw blade from said point A to said point B in a direction represented by an instruction code G2 or G3;   (4) determining number of pulses pA·A3, and pA·A4 necessary for rotating said fret saw blade from said point A to points A3 and A4 respectively in the same direction as that of the rotation of from point A to point B;   (5) determining smaller one of said pA·A3 and pA·A4;   (6) if the result of step 5 is pA·A3, then determining distance l13 between points A1 and A3 and distance l23 between points A2 and A3;   (7) if the result of step 5 is pA·A4, then determining distance l14 between points A1 and A4 and distance l24 between points A2 and A4; and   (8) if the result of step 6 or 7 is l13>l23 or l14>l24, then setting XP=XA1 and YP=YA1      whereas if l13<l23 or l14<l24, then setting XP=XA2 and YP=YA2.